mudtn/doxygen/a01076_source.html

/****************************************************************

 *

 * The author of this software is David M. Gay.

 *

 * Copyright (c) 1991 by AT&T.

 *

 * Permission to use, copy, modify, and distribute this software for any

 * purpose without fee is hereby granted, provided that this entire notice

 * is included in all copies of any software which is or includes a copy

 * or modification of this software and in all copies of the supporting

 * documentation for such software.

 *

 * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED

 * WARRANTY.  IN PARTICULAR, NEITHER THE AUTHOR NOR AT&T MAKES ANY

 * REPRESENTATION OR WARRANTY OF ANY KIND CONCERNING THE MERCHANTABILITY

 * OF THIS SOFTWARE OR ITS FITNESS FOR ANY PARTICULAR PURPOSE.

 *

 ***************************************************************/


/* Please send bug reports to

        David M. Gay

        AT&T Bell Laboratories, Room 2C-463

        600 Mountain Avenue

        Murray Hill, NJ 07974-2070

        U.S.A.

        dmg@research.att.com or research!dmg

 */


#include <ieeefp.h>

#include <math.h>

#include <float.h>

#include <errno.h>

#include <sys/config.h>

#include <sys/types.h>


#ifdef __IEEE_LITTLE_ENDIAN

#define IEEE_8087

#endif


#ifdef __IEEE_BIG_ENDIAN

#define IEEE_MC68k

#endif


#ifdef __Z8000__

#define Just_16

#endif


#ifdef DEBUG

#include "stdio.h"

#define Bug(x) {fprintf(stderr, "%s\n", x); exit(1);}

#endif


#ifdef Unsigned_Shifts

#define Sign_Extend(a,b) if (b < 0) a |= (__uint32_t)0xffff0000;

#else

#define Sign_Extend(a,b) /*no-op*/

#endif


#if defined(IEEE_8087) + defined(IEEE_MC68k) + defined(VAX) + defined(IBM) != 1

Exactly one of IEEE_8087, IEEE_MC68k, VAX, or IBM should be defined.

#endif


/* If we are going to examine or modify specific bits in a double using

   the word0 and/or word1 macros, then we must wrap the double inside

   a union.  This is necessary to avoid undefined behavior according to

   the ANSI C spec.  */

union double_union

{

  double d;

  __uint32_t i[2];

};


#ifdef IEEE_8087

#define word0(x) (x.i[1])

#define word1(x) (x.i[0])

#else

#define word0(x) (x.i[0])

#define word1(x) (x.i[1])

#endif


/* The following definition of Storeinc is appropriate for MIPS processors.

 * An alternative that might be better on some machines is

 * #define Storeinc(a,b,c) (*a++ = b << 16 | c & 0xffff)

 */

#if defined (__IEEE_BYTES_LITTLE_ENDIAN) + defined (IEEE_8087) + defined (VAX)

#define Storeinc(a,b,c) (((unsigned short *)a)[1] = (unsigned short)b, \

((unsigned short *)a)[0] = (unsigned short)c, a++)

#else

#define Storeinc(a,b,c) (((unsigned short *)a)[0] = (unsigned short)b, \

((unsigned short *)a)[1] = (unsigned short)c, a++)

#endif


/* #define P DBL_MANT_DIG */

/* Ten_pmax = floor(P*log(2)/log(5)) */

/* Bletch = (highest power of 2 < DBL_MAX_10_EXP) / 16 */

/* Quick_max = floor((P-1)*log(FLT_RADIX)/log(10) - 1) */

/* Int_max = floor(P*log(FLT_RADIX)/log(10) - 1) */


#if defined(IEEE_8087) + defined(IEEE_MC68k)

#if defined (_DOUBLE_IS_32BITS)

#define Exp_shift   23

#define Exp_shift1  23

#define Exp_msk1    ((__uint32_t)0x00800000L)

#define Exp_msk11   ((__uint32_t)0x00800000L)

#define Exp_mask    ((__uint32_t)0x7f800000L)

#define P           24

#define Bias        127

#if 0

#define IEEE_Arith  /* it is, but the code doesn't handle IEEE singles yet */

#endif

#define Emin        (-126)

#define Exp_1       ((__uint32_t)0x3f800000L)

#define Exp_11      ((__uint32_t)0x3f800000L)

#define Ebits       8

#define Frac_mask   ((__uint32_t)0x007fffffL)

#define Frac_mask1  ((__uint32_t)0x007fffffL)

#define Ten_pmax    10

#define Sign_bit    ((__uint32_t)0x80000000L)

#define Ten_pmax    10

#define Bletch      2

#define Bndry_mask  ((__uint32_t)0x007fffffL)

#define Bndry_mask1 ((__uint32_t)0x007fffffL)

#define LSB 1

#define Sign_bit    ((__uint32_t)0x80000000L)

#define Log2P       1

#define Tiny0       0

#define Tiny1       1

#define Quick_max   5

#define Int_max     6

#define Infinite(x) (word0(x) == ((__uint32_t)0x7f800000L))

#undef word0

#undef word1


#define word0(x) (x.i[0])

#define word1(x) 0

#else


#define Exp_shift  20

#define Exp_shift1 20

#define Exp_msk1    ((__uint32_t)0x100000L)

#define Exp_msk11   ((__uint32_t)0x100000L)

#define Exp_mask  ((__uint32_t)0x7ff00000L)

#define P 53

#define Bias 1023

#define IEEE_Arith

#define Emin (-1022)

#define Exp_1  ((__uint32_t)0x3ff00000L)

#define Exp_11 ((__uint32_t)0x3ff00000L)

#define Ebits 11

#define Frac_mask  ((__uint32_t)0xfffffL)

#define Frac_mask1 ((__uint32_t)0xfffffL)

#define Ten_pmax 22

#define Bletch 0x10

#define Bndry_mask  ((__uint32_t)0xfffffL)

#define Bndry_mask1 ((__uint32_t)0xfffffL)

#define LSB 1

#define Sign_bit ((__uint32_t)0x80000000L)

#define Log2P 1

#define Tiny0 0

#define Tiny1 1

#define Quick_max 14

#define Int_max 14

#define Infinite(x) (word0(x) == ((__uint32_t)0x7ff00000L)) /* sufficient test for here */

#endif


#else

#undef  Sudden_Underflow

#define Sudden_Underflow

#ifdef IBM

#define Exp_shift  24

#define Exp_shift1 24

#define Exp_msk1   ((__uint32_t)0x1000000L)

#define Exp_msk11  ((__uint32_t)0x1000000L)

#define Exp_mask  ((__uint32_t)0x7f000000L)

#define P 14

#define Bias 65

#define Exp_1  ((__uint32_t)0x41000000L)

#define Exp_11 ((__uint32_t)0x41000000L)

#define Ebits 8 /* exponent has 7 bits, but 8 is the right value in b2d */

#define Frac_mask  ((__uint32_t)0xffffffL)

#define Frac_mask1 ((__uint32_t)0xffffffL)

#define Bletch 4

#define Ten_pmax 22

#define Bndry_mask  ((__uint32_t)0xefffffL)

#define Bndry_mask1 ((__uint32_t)0xffffffL)

#define LSB 1

#define Sign_bit ((__uint32_t)0x80000000L)

#define Log2P 4

#define Tiny0 ((__uint32_t)0x100000L)

#define Tiny1 0

#define Quick_max 14

#define Int_max 15

#else /* VAX */

#define Exp_shift  23

#define Exp_shift1 7

#define Exp_msk1    0x80

#define Exp_msk11   ((__uint32_t)0x800000L)

#define Exp_mask  ((__uint32_t)0x7f80L)

#define P 56

#define Bias 129

#define Exp_1  ((__uint32_t)0x40800000L)

#define Exp_11 ((__uint32_t)0x4080L)

#define Ebits 8

#define Frac_mask  ((__uint32_t)0x7fffffL)

#define Frac_mask1 ((__uint32_t)0xffff007fL)

#define Ten_pmax 24

#define Bletch 2

#define Bndry_mask  ((__uint32_t)0xffff007fL)

#define Bndry_mask1 ((__uint32_t)0xffff007fL)

#define LSB ((__uint32_t)0x10000L)

#define Sign_bit ((__uint32_t)0x8000L)

#define Log2P 1

#define Tiny0 0x80

#define Tiny1 0

#define Quick_max 15

#define Int_max 15

#endif

#endif


#ifndef IEEE_Arith

#define ROUND_BIASED

#endif


#ifdef RND_PRODQUOT

#define rounded_product(a,b) a = rnd_prod(a, b)

#define rounded_quotient(a,b) a = rnd_quot(a, b)

#ifdef KR_headers

extern double rnd_prod(), rnd_quot();

#else

extern double rnd_prod(double, double), rnd_quot(double, double);

#endif

#else

#define rounded_product(a,b) a *= b

#define rounded_quotient(a,b) a /= b

#endif


#define Big0 (Frac_mask1 | Exp_msk1*(DBL_MAX_EXP+Bias-1))

#define Big1 ((__uint32_t)0xffffffffL)


#ifndef Just_16

/* When Pack_32 is not defined, we store 16 bits per 32-bit long.

 * This makes some inner loops simpler and sometimes saves work

 * during multiplications, but it often seems to make things slightly

 * slower.  Hence the default is now to store 32 bits per long.

 */


#ifndef Pack_32

#define Pack_32

#endif

#endif


#ifdef __cplusplus

extern "C" double strtod(const char *s00, char **se);

extern "C" char *dtoa(double d, int mode, int ndigits,

                        int *decpt, int *sign, char **rve);

#endif


typedef struct _Bigint _Bigint;


#if (defined (_SMALL_PRINTF) || defined(SMALL_SCANF) )

#define SMALL_LIB

#endif


#ifdef SMALL_LIB


#define small_Balloc    _small_Balloc

#define small_Bfree     _small_Bfree

#define small_multadd _small_multadd

#define small_s2b       _small_s2b

#define small_lo0bits _small_lo0bits

#define small_hi0bits _small_hi0bits

#define small_i2b       _small_i2b

#define small_mult      _small_multiply

#define small_pow5mult  _small_pow5mult

#define small_lshift    _small_lshift

#define small_cmp       __small_mcmp

#define small_diff      __small_mdiff

#define small_ulp       _small_ulp

#define small_b2d       _small_b2d

#define small_d2b       _small_d2b

#define small_ratio     _small_ratio


#define small_tens __small_mprec_tens

#define small_bigtens __small_mprec_bigtens

#define small_tinytens __small_mprec_tinytens


struct _reent ;

double          _EXFUN(small_ulp,(double x));

double          _EXFUN(small_b2d,(_Bigint *a , int *e));

_Bigint *       _EXFUN(small_multadd,(struct _reent *p, _Bigint *, int, int,_Bigint tab[]));

_Bigint *       _EXFUN(small_s2b,(struct _reent *, const char*, int, int, __ULong,_Bigint tab[]));

_Bigint *       _EXFUN(small_i2b,(struct _reent *,int,_Bigint tab[]));

_Bigint *       _EXFUN(small_mult, (struct _reent *, _Bigint *, _Bigint *,_Bigint tab[]));

_Bigint *       _EXFUN(small_pow5mult, (struct _reent *, _Bigint *, int k,_Bigint tab[]));

int             _EXFUN(small_hi0bits,(__ULong));

int             _EXFUN(small_lo0bits,(__ULong *));

_Bigint *        _EXFUN(small_d2b,(struct _reent *p, double d, int *e, int *bits,_Bigint tab[]));

_Bigint *        _EXFUN(small_lshift,(struct _reent *p, _Bigint *b, int k,_Bigint tab[]));

_Bigint *        _EXFUN(small_diff,(struct _reent *p, _Bigint *a, _Bigint *b,_Bigint tab[]));

int             _EXFUN(small_cmp,(_Bigint *a, _Bigint *b));


double          _EXFUN(small_ratio,(_Bigint *a, _Bigint *b));

#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))


#if defined(_DOUBLE_IS_32BITS) && defined(__v800)

#define n_bigtens 2

#else

#define n_bigtens 5

#endif


extern _CONST double small_tinytens[];

extern _CONST double small_bigtens[];

extern _CONST double small_tens[];


double _EXFUN(_small_mprec_log10,(int));


#else // NO SMALL_LIB


#define Balloc  _Balloc

#define Bfree   _Bfree

#define multadd _multadd

#define s2b     _s2b

#define lo0bits _lo0bits

#define hi0bits _hi0bits

#define i2b     _i2b

#define mult    _multiply

#define pow5mult        _pow5mult

#define lshift  _lshift

#define cmp     __mcmp

#define diff    __mdiff

#define ulp     _ulp

#define b2d     _b2d

#define d2b     _d2b

#define ratio   _ratio


#define tens __mprec_tens

#define bigtens __mprec_bigtens

#define tinytens __mprec_tinytens


struct _reent ;

double          _EXFUN(ulp,(double x));

double          _EXFUN(b2d,(_Bigint *a , int *e));

_Bigint *       _EXFUN(Balloc,(struct _reent *p, int k));

void            _EXFUN(Bfree,(struct _reent *p, _Bigint *v));

_Bigint *       _EXFUN(multadd,(struct _reent *p, _Bigint *, int, int));

_Bigint *       _EXFUN(s2b,(struct _reent *, const char*, int, int, __ULong));

_Bigint *       _EXFUN(i2b,(struct _reent *,int));

_Bigint *       _EXFUN(mult, (struct _reent *, _Bigint *, _Bigint *));

_Bigint *       _EXFUN(pow5mult, (struct _reent *, _Bigint *, int k));

int             _EXFUN(hi0bits,(__ULong));

int             _EXFUN(lo0bits,(__ULong *));

_Bigint *        _EXFUN(d2b,(struct _reent *p, double d, int *e, int *bits));

_Bigint *        _EXFUN(lshift,(struct _reent *p, _Bigint *b, int k));

_Bigint *        _EXFUN(diff,(struct _reent *p, _Bigint *a, _Bigint *b));

int             _EXFUN(cmp,(_Bigint *a, _Bigint *b));


double          _EXFUN(ratio,(_Bigint *a, _Bigint *b));

#define Bcopy(x,y) memcpy((char *)&x->_sign, (char *)&y->_sign, y->_wds*sizeof(__Long) + 2*sizeof(int))


#if defined(_DOUBLE_IS_32BITS) && defined(__v800)

#define n_bigtens 2

#else

#define n_bigtens 5

#endif


extern _CONST double tinytens[];

extern _CONST double bigtens[];

extern _CONST double tens[];


double _EXFUN(_mprec_log10,(int));


#endif